Question: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\dfrac{5}{8}$ $a_i = 2a_{i-1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{5}{8}$ and the common ratio is $2$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{5}{8} \cdot 2 = -\dfrac{5}{4}$.